# Visualizing the Area of a Circle and its Formula

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Exploration

GR. 6-8

Skill:

Use models to develop formulas for finding areas of triangles, parallelograms, trapezoids, and circles in number and word problems.

# Visualizing the Area of a Circle and its Formula

Develop the formula for finding the area of a circle by breaking a circle into pieces and rearranging them.

### Putting It All Together

Answer these open ended questions on your own or with others to form deeper math connections.

### Open-ended question 1

When the circle is rearranged and the number of parts increases, what shape do the rearranged parts start to look like?

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### Open-ended question 2

The formula for the area of a parallelogram is . If a circle is rearranged into many parts that appear like a parallelogram, what is the measure of the height and what is the measure of the base?

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### Open-ended question 3

How does the formula for the area of a circle relate to the formula for the area of the parallelogram created by rearranging the sectors of the circle?

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